Why do many top bankers use fast speed?With faster speed, there is much less variation from table to table and from shot to shot. The OB will pick up less roll, and this (combined with the post rebound speed) will minimize how much the OB curves after rebound. As a result the ball will bank in a more consistent direction.Also, there are many variables that affect how a ball banks (cloth friction, cushion friction and coefficients of restitution, OB spin transfer, and table roll-off). At faster speed, these variables don't change the shot as much with slight changes in speed as they do with similar speed changes at slower speeds. This is another advantage of using faster speed for banks.At slower speeds, the path and final target of the rebounding ball varies a lot with small changes in speed. The disadvantage of faster speed is the reduced effective "size" of the pocket.Faster speed can also help reduce the chance for a double kiss at certain approach angles. See:

How do you aim to kick at balls close to a rail at a shallow angle into the rail?For shallow angles into the rail, where the OB is fairly close to the rail, the contact-point-mirror-kick method works well. It is described in "VEPS GEMS - Part VII: Contact-Point Mirror Kick" (Download) (BD, July, 2010) and “VEPP – Part X: Shallow One-rail Kicks” (Download) (BD, January, 2013), and here are video demonstrations with a complete explanations:

﻿f﻿rom Patrick Johnson:[Here's] a simplified way to estimate 3-rail kicks to given targets on the fourth rail. This simplified 3-rail kick system is vaguely similar to the Spot-On-The-Wall system and the Corner-Five system, but instead of off-table visual references (Spot-On-The-Wall) or math (Corner Five), it uses simple diamond-to-diamond alignments.

Three rail kicks that start out parallel to each other (their first legs are parallel) end up hitting the fourth rail very close together - they "converge" on a fourth rail target. It's easy to see parallel lines on the pool table using the diamonds. If we start with a line stretched between one diamond on the near long rail and another diamond on the far long rail, we can simply move each end of the line one diamond to the right to find a parallel line. Move each end another diamond in the same direction (left or right) and there's another parallel line, etc. The angle of these parallel lines between the diamonds is determined by how many diamonds along the rail one diamond is from the other - call this their "separation". For instance, diamonds on opposite long rails with "4 diamonds of separation" make parallel lines at 45 degrees (see third diagram below), while diamonds with "3 diamonds of separation" make parallel lines at 51 degrees (see fourth diagram below).

Using these easy-to-see diamond-to-diamond lines, we get sets of parallel lines to use as reference tracks for 3-rail kicks. Fortunately for us, each set of parallel lines converges near a pocket or diamond on the fourth rail, making both our first legs and our fourth rail targets easy to remember. The correlations are:

- a first leg line with 6 diamonds of separation will come close to the corner pocket on the fourth rail- a first leg line with 5 diamonds of separation will come close to the 1st diamond on the fourth rail- a first leg line with 4 diamonds of separation will come close to the 2nd diamond on the fourth rail- a first leg line with 3 diamonds of separation will come close to the 3rd diamond on the fourth rail

Below are diagrams illustrating these basic reference tracks:

Use a "6-diamond separation" to hit the corner pocket on the 4th rail.

(Click to enlarge)

Use a "5-diamond separation" to hit the 1st diamond on the 4th rail.

(Click to enlarge)

Use a "4-diamond separation" to hit the 2nd diamond on the 4th rail.

(Click to enlarge)

Use a "3-diamond separation" to hit the 3rd diamond on the 4th rail.

(click to enlarge)

from AtLarge:I think this will be extremely easy to remember. Notice that for each of the cases you cited, the number of diamonds of separation plus the 4th-rail convergence diamond (counting from the pocket as zero) totals 6. That is, 6+0=6. 5+1=6. 4+2=6. 3+3=6. So we could call it the "Sixes System" for three-rail kicks.

from freddy the beard: Determining whether a bank shot lays in the "kiss" zone is often misunderstood, and usually winds up as an educated guess. In the following diagrams I have outlined exactly when a bank cannot normally be made using a rolling with or without english. In diagram #1, I deal with the shorter angle cross-corners. If the straight-in angle of the cueball and object ball is lined up and aiming into the pocket facing, the shot is a certain kiss. Left or right english, follow, center, or draw is not going to help you beat that kiss. With a slight angle adjustment, as per diagram #2, lined up to the middle of the back of the pocket, the bank can now be easily made with rolling or center ball, no english. Diagram #3 is another variation that must be considered. It involves crossing, or passing-over, the object ball from a much more severe angle. Rather than calculate off of a straight-in angle as per dia.#1 & 2, the kiss/no kiss reference point is determined by lining up the actual cut angle needed to make the bank. If an imaginary line from the center of the cueball, extending thru the cut area on the object ball, continues into the middle of the back of the pocket, the kiss is "on." If the line instead, is aiming at the short/bottom rail, you can go ahead and shoot the shot with impunity. Provided of course you are using a natural rolling ball, center ball, left english in this case, or draw. Right hand english when the bank is "on" could result in a kiss.

What effects does one need to adjust for when aiming bank and kick shots? First, "VEPS GEMS - Part XVII: Trick and Proposition Shots" (Download) (BD, May, 2011) and the video below illustrate, describe, and demonstrate basic terminology for bank and kick shots:

The basic mirror (angle in equals angle out) systems provide a point of reference only. Your aim with a given shot depends on many effects. The effects that require aim adjustment include:

In general, more speed shortens the rebound (﻿s﻿ee ﻿﻿NV 6.﻿6﻿), and less speed lengthens the rebound (see ﻿NV 6﻿.7); however, see HSV B.41 (YouTube) and NV B.95 (YouTube). One reason faster speed shortens a rolling-CB, angled kick is that the post-rebound curve is delayed by the speed. With a fast-speed, small-angle bank, the OB has near stun into the cushion and picks up topspin off the rail (see HSV B.15 (YouTube)), which curves the OB short.

Running english lengthens rebound, and reverse english shortens the rebound (see NV 6.8). This effect is greatest with the ball heading straight into the rail (i.e., with no approach angle).

Running english results in more CB speed after rebound, and reverse english results in less CB speed after rebound. The difference is greatest at a moderate approach angle in the rail (i.e., about 20-40 degrees from the rail perpendicular). See also: rail cushion speed changes.

English has little effect at large approach angles, where the ball is heading fairly parallel to the rail (e.g., see HSV A.71). However, the english will have a large effect off the second rail, where the approach angle will be small, with the ball heading fairly perpendicular to the rail.

Spin transfer can significantly affect banks (e.g., left spin on the CB can transfer right spin to the OB which shifts the rebound to the right).

If the CB has a "natural english" amount (similar to "gearing english" for a cut shot), the sidespin won't change off the cushion. With less sidespin (including "negative" or reverse english), the cushion will increase the amount of spin, and the angle will shorten (e.g., see HSV 6.5); and for more english, the spin will decrease off the cushion, and the angle will lengthen (e.g., see HSV A.28).

Cut and spin transfer effects are related to throw effects, so a complete understanding of throw helps too.

Kicks and banks generally go longer on new and clean in a dry environment (see cloth effects for more info).

If one doesn't understand all of these effects, or have great intuition built up from years and years of experience (i.e., lots of mistakes and successes), the mirror systems are not very useful. Here's an excerpt from Disc IV of the Video Encyclopedia of Pool Practice (VEPP) (external web-link) that shows you how to develop a feel for some of the effects during practice:

For kick shots with small approach angles (i.e., almost straight into the rail), it sometimes helps to know how topspin and bottom-spin change off the rebound. For more information and examples, see:

from Patrick Johnson: For kicks the important thing is what kind of "vertical spin" the CB has on it when it hits the rail: - CB sliding when it hits the rail will rebound with no curve at the "mirror angle" (minus something for rail friction) - CB with forward spin (including natural roll) when it hits the rail will curve longer than the mirror angle - CB with backspin when it hits the rail will curve shorter than the mirror angle How much longer or shorter the CB rebounds (with forward spin or backspin) depends on how much spin is on the CB* and how much friction there is between the CB and the cloth. For banks the important thing is how much vertical spin is on the OB when it hits the rail. This can only be controlled by hitting harder or softer (harder = less or no forward spin; softer = more forward spin). This is also why hitting harder shortens bank angles. *: How much spin is on the CB depends on: - how hard it's hit - how high it's hit - how far it is from the rail when it's hit - how much friction there is between CB/cloth

(Click to enlarge)

As this drawing shows, when the CB changes direction off the rail its spin does not change direction. That means that forward or reverse spin which was rotating parallel with the CB's path before hitting the rail is rotating across the CB's path after hitting the rail - this across-the-path rotation is what causes the CB to curve after hitting the rail.

Forward rotation (topspin) can be the result of the CB rolling naturally or of hitting high on the CB. Reverse rotation (backspin) can only be the result of hitting low on the CB.Concerning HSV B.41 (YouTube), why doesn't speed shorten the rebound angle? Doesn't the ball compress the cushion sideways more at higher speed, and wouldn't that create sideways forces that would shorten the rebound angle? There are many physical effects that control the immediate rebound angle and the amount of masse curving after rebound. I use the phrase "rail throwback" to refer to the effect you are describing. With more speed the cushion deforms more and can generate more sideways force to shorten the angle; however, the rebound angle is also affected by the efficiency (coefficient of restitution = COR) of the cushion, and this can vary with speed and angle also. Based on the results in HSV B.41(YouTube), these two effects are balancing each other out. The rail throwback effect tries to shorten the rebound angle and the efficiency effect apparently tries to lengthen the rebound (because the cushion is returning less energy, maybe partly because of the ball shift down the rail). This is all conjecture, but it makes sense physically. There are also friction effects between the ball and cushion and ball and table during impact. These might also vary in complicated ways with speed.

How does the basic mirror system work? "VEPS GEMS - Part V: Banks and Kicks" (Download) (BD, May, 2010) and the video below illustrate, describes and demonstrates the basic terminology for bank and kick shots, and explains the basic equal-rail-distance mirror system:

The basic mirror (angle in equals angle out) systems provide a point of reference only. You must compensate your aim for a given shot based on the many effects and factors to consider. For shallow angle kicks, where the object ball is close to the rail, the following mirror system works quite well:

from Patrick JohnsonAZB post: (external forum-link)Here are the reference angles for banking/kicking to the bottom left corner pocket - they connect each 1/2 diamond on the far rail with the whole diamond twice as far along on the near rail:

﻿Of course, I don't visualize all these reference angles for every shot to that corner. For instance, the 2 ball is very near one reference angle, so I'll just compare it to that one:﻿

﻿The 1 ball is midway between two reference angles, so I'll compare it to both of them:﻿

﻿Here's the same technique applied to kicking at a ball that's not on the near rail. Just move the near "rail" (where you measure the whole diamonds) up to be parallel with the target - it doesn't matter if the cue ball is above or below the adjusted "rail".﻿

﻿Here's another way of measuring kick shots, a little different from the "reference angles" method I posted earlier, but using the same 2-to-1 principle. It should be self explanatory...﻿

﻿Like the "reference angles" this measures the "equal angle" kick, so of course you need to adjust for cloth stickiness & ball speed/spin.﻿

How do adjust your aim for a fast-speed bank?The simplest approach is to use the basic mirror system and shift the butt of the cue by about 1/3 diamond, as described in "VEPS GEMS - Part V: Banks and Kicks" (Download) (BD, May, 2010). Here's the diagram from the article that illustrates how the system works:

(Click to enlarge)

The butt shift alone works only when the OB is fairly close to the banking rail. But regardless of the distance to the rail, after adjusting the mirror aim, the line of action of the OB should cross the origination rail groove at a point about 1/3 to 1/2 diamond more than twice the distance on the banking rail. In the example above, the final line of the OB should be aimed at about 1.9 and originate from about 4.3 (2*1.9 + 0.5). The exact amount of adjustment needed will vary with conditions and the angle of the bank, but 1/3 of a diamond is a good general benchmark reference.Another useful fast-speed banking reference is the 3-to-1 line. On most tables, shooting through 1 from 3 with very fast speed pockets the ball.An alternative to the 1/3-diamond system described above is a through-diamond system described in the following video: Ekert's bank shot reference lines (YouTube). It can be described concisely as the "2x-to-3/4x-through-diamond system" as opposed to the "(2x+1/3)-to-x rail-grove system" described above. Both systems are described and illustrated in detail in: “Fast Speed Banks”(Download) (BD, July, 2013).In addition to being able to use the aiming systems above, there are advantages to using fast speed with bank shots. For more info, see: advantages of fast speed.

How do you aim shallow-angle kick shots where the object ball is close to the rail?When the object ball is close to a ball away from the rail, the following mirror system, from Disc IV of the Video Encyclopedia of Pool Shots (VEPS) (Download) is very effective:

What is the "Sid System" and how does it work?from Bob Jewett (from AZB post):(external forum-link)For those who are wondering what "System Sid" is, here is the diagram from Walt Harris's book, "Billiard Atlas". To hit a spot on the second cushion, multiply the number for the spot by how many diamonds the cue ball is from point X. In the example, the target is 2.5 and the cue ball (Q) is 3 diamonds from X so the target is 7.5 on the short rail. Note that the short rail (M) is numbered 10 to the diamond, the second rail has a variable numbering that you have to memorize, and the rail you are shooting from (O) is numbered in units to multiply with. Harris recommends renumbering the O rail according to the second rail number, so in the example it would be numbered 0, 2.5, 5.0 and 7.5 starting from X.

If you work out the geometry in detail, the numbers on the second rail are off a little but as listed they are easy to remember.

Is spin transfer required to make certain bank shots?Yes. See NV B.20 (YouTube) for two important examples. For more information, and another example, see "Throw - Part VIII: spin transfer" (Download) (BD, March, 2007). Many more examples of spin-transfer shots, can be found here: Spin Transfer

How do "spot-on-the-wall" kicking systems work?The three-rail Corner-5, two-rail Plus-2, and one-rail kick "spot-on-the-wall" systems are described and demonstrated here:

More information, including guidelines on how far the spot would be from the table, can be found in "VEPS GEMS - Part XIV: 'Spot-on-the-Wall' System" (Download) (BD, February, 2011).There are different "rules of thumb" for estimating the best distance to the spot on the wall, but they don't always match the results in the article (Download) very well. Here's a common rule that does a decent job (although, it predicts a distance longer than recommended for a 3-rail shot and a distance shorter than recommended for a 1-rail shot):from Monte Ohrt:For any given spot-on-the-wall kick shot, the exact optimal distance from the first rail to the spot is the distance the cueball travels after it hits the first rail to the target. For a one-rail kick, this is simply the distance from rail 1 to the target. For a two-rail kick, it is the distance between rail 1 and 2, and also add the distance between rail 2 and the target point. For a three rail kick, it is the distance between rails 1 and 2, 2 and 3, and 3 to the target point ... and so on for 4 rails, 5 rails, etc. After about 3 rails the point of convergence is so narrow that it normally doesn't make any difference, just pick a spot at least 3 tables away.

Is there an aiming system for two-rail bank shots off the short rail?You can use the Plus System for aiming two-rail banks off the short rail, but it will require practice to learn how to adjust for the lack of running english and forward roll on the OB into the first cushion which varies with distance and shot speed.If the OB is fairly close to or frozen to the short rail, the systems below from Freddy Bentivegna work fairly well.from freddy the beardAZB post: (external forum-link)

Dr. Dave, I have been practicing the 2-rail parallel line kick shots you show in your book on pages 229 & 230 and demonstrated in NV 7.9. It works fine if I set up the balls similar to what you show in your book but I am having difficulty envisioning the same shot from other set ups. I don't think I fully understand how to determine the center line between the 2 parallel lines. Can you elaborate on this idea?

Unfortunately, the action of this shot depends on english, shot speed, and table (especially cushion) conditions. Obviously, when practicing, you need to try to use consistent english and speed on a given table to see how the cue ball responds at different angles.For more information and demonstrations, see Shots 514 and 515 on Disc IV of the Video Encyclopedia of Pool Shots. (external web-link)from Patrick Johnson:You have to aim a little closer to the corner than the measurement suggests - experience will tell you how much, depending on the angle to the first rail and the cleanliness of the table/balls.

In this drawing the blue line is the measured track, but the actual track will look more like the red line:

(Click to enlarge)

from Bob_Jewett:... the "Amazing Double-mirror Image Method" or ADIM for short ... is explained on the second page of http://www.sfbilliards.com/articles/2004.pdf (July). (Download) Mostly, it gives you a very easy way to put up a target ball exactly where the real ball would appear for a perfect mirror system. ... This lets you see immediately how pitifully awful the two-rail mirror system is, but it also allows you to try to find out where it does work and maybe how to modify it so it works for more cases.

What are "two-times" and "three-times" across bank shots, and how do they work?

See:

from Patrick Johnson:It's a series of spin events:1. The CB colliding with the OB puts some "holdup" spin on the OB, which shortens the angle off the first rail.2. The OB colliding with the first rail at an angle reverses the spin that was put on by the CB (just like any ball picks up "running" spin when it hits the rail).3. The reversed spin throws the OB toward the side pocket off the second rail.